A linear chirp is induced through a quadratic phase-modulation process. A primary issue for the generation of the linearly-chirped pulses shown in Fig. 3.2 is, therefore, the large quadratic phase-modulation required to sufficiently broaden the spectrum of the long rectangular pulses. For instance, the pulses in Fig. 3.2 have a total
-4 -2 0 2 4 300 200 100 0 Spectrogram -40 -35 -30 -25 -20 -15 -10 -5 0 Rel. Power (dB)
Figure 3.2: Ideal linearly-chirped pulse to enable TDM-WDM conversion at the base bit-rate of 10 Gb/s.
phase-shift of 100πrad. Long rectangular pulses can easily be generated by externally modulating the intensity of a CW laser beam, and electro-optic phase modulators can be used to induce a quadratic phase-modulation. However, state-of-the-art electro- optic phase modulators can induce at most a total phase-shift of about 15π rad. In [81] the generation of highly linearly-chirped pulses using an integrated LiNbO3 phase and intensity modulator, which externally modulates a CW laser beam to produce 50-ps Gaussian pulses with a bandwidth of 7 nm at the repetition rate of 10 GHz, was demonstrated. Generation of broader bandwidth pulses using this technology is, however, a challenging research goal. The above results required the fabrication of a remarkably long 15-cm LiNbO3 waveguide, which was driven at 10 GHz with an RF power of 36 dBm to achieve the 15π-rad phase modulation index. Nonetheless, low drive voltage LiNbO3 phase and intensity integrated modulators are a great research achievement and several applications, including the techniques proposed in this thesis, can benefit from this compact source of highly linearly-chirped pulses.
Large frequency modulation (chirp) in optical pulses can also occur through excitation of the fibre nonlinearities. For example, self-phase modulation (SPM) occurs when the pulse itself induces variation of the medium’s refractive-index resulting in a change in the phase of the pulse across the pulse envelope due to the intensity variation. During this process new spectral components are generated and the pulse suffers spectral broadening. The efficiency of the SPM effect depends directly on the pulse’s
Section 3.2. Chapter 3
intensity profile and on the nonlinear coefficient of the medium. However, the group velocity dispersion (GVD) of the medium also chirps the pulse, and the interplay between GVD and SPM determines the pulse evolution. Briefly, if SPM dominates in the anomalous dispersion regime the pulse evolves into a higher-order soliton, while in the normal dispersion regime the chirp due to SPM and GVD add together, which opposes the formation of soliton pulses.
Ultra-wide spectral broadening spanning several hundreds of nanometers has been reported by many research groups based on supercontinuum generation processes. However, pulse breakup, and phase coherence degradation can be severe during the generation process if the spectrum extends into the anomalous dispersion regime. Even at high repetition rates (higher than 1 GHz), where the relatively low pulse energies induce only Kerr nonlinear refractive effects, phase coherence can be severely degraded by modulational instability [82, 83].
For the generation of spectral broadening suitable for telecommunications appli- cations, the use of either dispersion decreasing fibres (DDF) [84], or low normal- dispersion dispersion-flattened fibres (ND-DFF) [85] has been reported. The use of DDFs can give significant spectral broadening. For example, in [86] the generation of 1µm broad supercontinuum in a nonlinear DDF, from 110-fs pulses emitted by a passive mode-locked fibre laser at a wavelength of 1550 nm is reported. However, in the DDF the flatness of the spectrum is usually compromised by higher-order soliton effects unless adiabatic soliton compression is used. The schemes employing ND- DFFs take care to ensure that the zero dispersion wavelength of the fibre lies well outside the generated wavelength range in order to avoid the onset of modulational instability, which may also compromise the achievable spectral flatness. Several high speed signal processing schemes have been proposed based on the wide, flat super- continuum generated in ND-DFF [87]. This fact led us to investigate chirped pulse generation in the normal dispersion regime of the dispersion shifted highly nonlinear fibres shown in Table 2.1.
The first measurements we carried out to characterise the chirp generation in these fibres, involved measuring the achievable spectral broadening of 2.5-ps transform limited pulses generated from an actively mode-locked fibre laser at a repetition rate of 10 GHz; the experimental setup is shown in Fig. 3.3. The pulses were externally modulated with a pseudo-random bit-sequence (PRBS), so that higher pulse energies
Mode-locked Fibre Laser HNLF OSA MOD EDFA Pattern Generator 10 GHz
Figure 3.3: Experimental setup to characterise spectral broadening in a HNLF.
could be achieved due to the presence of zeros in the bit stream. The pulses were then amplified to an average power of 19 dBm and launched into the highly nonlinear fibre. Fig. 3.4 shows the measured broadened spectra for the HNL-DSF2, HNL-DFF2, and HNL-DFF3 fibres in Table 2.1. In cases (a) and (b) the pulses were launched in the normal dispersion regime. In both cases, the broadened spectrum had a −3- dB bandwidth of roughly 20 nm, however, the larger dispersion slope of HNL-DSF2 induced asymmetrical broadening of the spectral envelope relative to the seed pulse centre wavelength. The original spectral band of the seed pulses is shown in the dashed trace.
In case (c), the pulses were launched in the anomalous regime of HNL-DFF3. Al- though the small dispersion-slope ensures symmetrical spectral broadening, large rip- ples in the spectral envelope are the consequence of higher-order soliton formation. Furthermore, the degradation of the spectral lines in comparison to the previous cases is strikingly clear, which indicates a degradation of the pulse-to-pulse temporal co- herence. Note that in this case, the launched average power was limited to 15 dBm to avoid the complete suppression of the spectral lines.
The physical reason for the spectral ripples is that the same frequency appears at different instants across the pulse, which leads to spectral interference that is different for different frequencies. In the case of nonlinear chirping in the anomalous regime, there is a larger contribution to the interference as the induced chirp is oscillating across the full pulse envelope. By contrast, in the normal regime the chirp oscillates just at the pulse edges, and therefore the interference effects are smaller.
It was, therefore, observed that HNL-DSF2 and HNL-DFF2 are more suitable fibres to generate spectrally broad linearly-chirped pulses. At the early stage of this thesis
Section 3.2. Chapter 3 1530 1540 1550 1560 1570 1580 1530 1540 1550 1560 1570 1580 1530 1540 1550 1560 1570 1580 (a) (b) (c) Dispersion < 0 Dispersion < 0 Dispersion > 0
Figure 3.4: Measured spectral broadening of 2.5-ps pulses with an average power of (a) 19 dBm at the repetition rate of 10 GHz in HNL-DSF2, (b) 19 dBm at the bit-rate of 10 Gb/s in the HNL-DFF2, (c) 15 dBm at the bit-rate of 10 Gb/s in the HNL-DFF3. The dashed trace shows the spectrum of the seed pulse.
work, only HNL-DSF2 was available, and we proceeded at that time with investigating the phase and amplitude of the spectrally broadened pulses. The characterisation
of the complex amplitude of short pulses can be determined from a spectrogram of the pulse intensity. A widely established technique to measure spectrograms is frequency-resolved optical-gating based on the second-harmonic generation (SHG- FROG) of the pulses under test, or in other words the pulse frequency resolved autocorrelation. However, to characterise broad spectrum pulses it is necessary to use a nonlinear SHG crystal that provides phase matching across the full bandwidth of the pulses. Broadband phase matching requires a thin crystal to minimize the group velocity mismatch between the second harmonic and the pump pulses, while high SHG efficiency at the 10-GHz pulse rate requires the crystal material to be strongly nonlinear. Unfortunately, the SHG-FROG in our lab has a standard crystal, and thus we were unable to use this technique to characterise experimentally the pulses shown in Fig. 3.4.
Consequently, we proceeded by numerically simulating the pulse electric-field using the modelling techniques described in Chapter 2. The HNL-DSF2 parameters con- sidered in the numerical simulation are shown in Table 2.1.
The model was based on solving the nonlinear Schr¨odinger equation using the sym- metric split-step Fourier algorithm taking into account the fibre attenuation, group- velocity dispersion, dispersion slope and the nonlinear Kerr effect. Considering the relatively low pulse energy available at the 10-GHz repetition rate, and to simplify the analysis, the effects of stimulated Raman scattering and self-steepening were ne- glected.
The main advantage of the split-step Fourier algorithm compared to other meth- ods is the possibility of computing the complex amplitude of the pulses in time and frequency domains at different distances along the fibre in one simulation run. It is, therefore, a good tool to study pulse envelope and spectral evolution in the fi- bre. Fig. 3.5 shows the spectrogram of the pulses generated in the HNL-DSF2, when 2.5 ps sech2-shaped pulses with an energy of about 10 pJ are launched into the fibre. The figure also shows the corresponding pulse envelope and spectrum. The calcu- lated spectrum shows good agreement with the measured spectrum in Fig. 3.4(a). During propagation in the normal dispersion regime of a nonlinear fibre, the pulses evolve initially into a parabolic shape and deform later into a square-like form. The pulse full-width at half-maximum (FWHM) evolution in the HNL-DSF2 is shown in Fig. 3.6(b). It can be seen that the pulse duration broadens from 2.5 ps to 8 ps.
Section 3.2. Chapter 3
The calculated pulse envelope shows a negative slope on the top towards the trailing edge. The explanation is that the trailing edge is composed of lower frequencies, which travel faster, and therefore the dispersive effects are more significant in this part of the pulse.
Time (ps) -4 -2 0 2 4 20 10 5 0 Spectrogram
optical wave breaking optical wave breaking
15
Figure 3.5: Spectrogram of the chirped pulses generated in HNL-DSF2 and correspond- ingtime and frequency marginals.
20 5 0 Power(a.u.) 15 Chirp(THz) 0 1.5 -1.5 Time (ps) 10 2 3 4 5 6 7 8 0 0.1 0.2 0.3 0.4 0.5 z (km) FWHM(ps)
Figure 3.6: (a) Linearly-chirped pulse generated in HNL-DSF2. (b) Pulse duration evo- lution along the fibre length.
Optical wave breaking occurs when the leading and trailing edges of the pulse overlap the unchirped components in the pulse wings [88]. Consequently, different frequen- cies with a phase difference overlap temporally, and an oscillating intensity envelope
develops at the pulse wings. This is associated with the formation of spectral side lobes in the pulse spectrum. In the case of HNL-DSF2, shown in Fig. 3.5, the group- velocity dispersion is higher for the higher frequency components due to the large dispersion-slope of the fibre and, as the pulse trailing edge consists of higher fre- quencies, optical wave breaking occurs first at the trailing edge. In Fig. 3.6(a), the pulse generated at the output of HNL-DSF2 and its corresponding frequency chirp are shown; the effect of the dispersion slope in the chirp linearity is clearly evident. Having discussed in this section the reasons that led us to choose spectral broadening in the normal dispersion of highly-nonlinear dispersion-shifted fibres, I proceed in the next section to describe the stretching of the envelope of these pulses.